User-defined function interpolation

Is there a way in matlab to interpolate data with an user defined fuction? I mean, I can use linear interpolation, cubic etc.. and it's easy, but what if I wanted to interpolate with another function? e.g sine, or cosine or whatever.

Let's imagine we have some data and an user defined function, f(x)

x=0:0.01:10;

y=randn(size(x));

k=1:1:(size(x(:)));

I know that an interpolation must satisfy f(x(k))=y(k) for every k but i can't go much further, any help would be appreciated